In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar, baking powder, cinnamon, and baking soda. Beat until combined, scraping side of bowl occasionally. Beat in the 2 egg whites and the vanilla until combined. Beat in as much of the all-purpose flour and whole wheat flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour and the oats. Cover and chill dough about 2 hours or until easy to handle.